Best Known (110−25, 110, s)-Nets in Base 9
(110−25, 110, 1103)-Net over F9 — Constructive and digital
Digital (85, 110, 1103)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (73, 98, 1093)-net over F9, using
- net defined by OOA [i] based on linear OOA(998, 1093, F9, 25, 25) (dual of [(1093, 25), 27227, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(998, 13117, F9, 25) (dual of [13117, 13019, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(998, 13124, F9, 25) (dual of [13124, 13026, 26]-code), using
- trace code [i] based on linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- trace code [i] based on linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(998, 13124, F9, 25) (dual of [13124, 13026, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(998, 13117, F9, 25) (dual of [13117, 13019, 26]-code), using
- net defined by OOA [i] based on linear OOA(998, 1093, F9, 25, 25) (dual of [(1093, 25), 27227, 26]-NRT-code), using
- digital (0, 12, 10)-net over F9, using
(110−25, 110, 1640)-Net in Base 9 — Constructive
(85, 110, 1640)-net in base 9, using
- net defined by OOA [i] based on OOA(9110, 1640, S9, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(9110, 19681, S9, 25), using
- discarding factors based on OA(9110, 19686, S9, 25), using
- discarding parts of the base [i] based on linear OA(2773, 19686, F27, 25) (dual of [19686, 19613, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(2773, 19683, F27, 25) (dual of [19683, 19610, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(2773, 19686, F27, 25) (dual of [19686, 19613, 26]-code), using
- discarding factors based on OA(9110, 19686, S9, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(9110, 19681, S9, 25), using
(110−25, 110, 28978)-Net over F9 — Digital
Digital (85, 110, 28978)-net over F9, using
(110−25, 110, large)-Net in Base 9 — Upper bound on s
There is no (85, 110, large)-net in base 9, because
- 23 times m-reduction [i] would yield (85, 87, large)-net in base 9, but